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Platelet counting by light diffraction
Volume 10, number 3
OPTICS COMMUNICAFIONS
March 1974
P L A T E L E T C O U N T I N G BY L I G H T D I F F R A C T I O N J.P. MERIC and J.F. CARON Ci'ntre d'Etudes et de Recherches de l 'lndustrie des Liants tt3,drauliques, 23 rue de Cronstadt, 75015 Paris, France
an d M. GOUAULT-HEILMANN and C. SULTAN Service Central d7tOnatologie-hnmunologie. Hopital Henri Mondor, 94010 Creteil. France
Received 4 January 1974 Optical properties of platelets have yet been studied by light transmission in order to follow their shape transformation. The experiments described here deal with platelet diffraction measurements performed with coherent and monochromatic laser light. The purposes of the assay which have been done, tend to demonstrate that the optical properties of platelets allow to perform counting with accuracy.
Tile device used is an optical system including a laser source, imaging lenses, a sample holder and a power spectra analyser (fig. 1). It is well known [21 that tile analysis of the light diffracted by the particles contained in tile sample holder permits to obtain statistical data about these particles. The diffracted light is measured in tile I~cal plane of the optical system, the so-called Fourierplane. It is composed of a central peak of direct light. This peak is surrounded by diffracted light which is spread around it. The Fraunhofer diffraction pattern in the Fourier-plane can be computed by Fourier transformation of the transmission and phase distribution of the array formed by the particles contained in the sample holder. The particles considered here are the blood cells of whole blood after hemolysis of the red cells. These particles are: ghosts of red cells, white cells, and platelets. The ghosts of red cells have a refraction index which is quite near to the index of the medium. This originates an amount of diffraction which is very weak for each particle but tile ghosts are very numerous and therefore the total amount of diffraction that is originated by them becomes very important. The ghosts of red cells are perfectly spherical. Their diffraction pattern can be calculated with high accuracy 266
according to the formula [3] ,S'(s)=Cf(1
e ipsinr) e ik~sd~dn,
where S is the amplitude function of the diffracted light, s is tile angle (fig. 1), k = 27r/•, X is the wavelength of the incident radiation, a is the radius of the particle, r is defined b y a 2 cos 2 7- = ~2 + n 2, and Cis a constant. Tile integral is taken over tile area of a circle with radius a. Tile intensity of tile diffraction pattern of a collection of particles is tile sum of the intensity related to each single particle if there is no overlapping in tire position of each cell. In effect there is some overlapping in position especially for ghosts of red cells. We have used a rather sophisticated mathematical model (overlapping circular grain model) to take this facl into account [21. Tile white cells are quite irregular in shape but they do not differ too much from the sphere. The size ranges from 15 to 9/ira. Light absorption in the cells is also very irregular but this may be practically neglected. Tile platelet size is 3 /lln. This dimension is near the wavelength of the light which we have used (0.63 ~m). Therefore scattering does not depend very much on the shape.
Volume 10, number 3
OPTICS COMMUNICATIONS
March 1974
diffracted light lenses
~
Et direct light
sample h o l d e r
Laser
Fig. 1. Optical system. The three kinds of particles described above scatter the light in a manner which is directly related to their size. The total diffraction pattern is the sum of the pattern of the three kinds o f particles. These patterns are described in figure 2. The horizontal axis represents the radius in the Fourier plane corresponding to the diffraction angle s. High values of the radius represent low spatial frequencies in the sample holder and low values represent very high spatial frequencies. Our experiments consisted in measuring the total energy comprised between two angles, s 1 and s 2 for example, and to relate them to the total number o f platelets, white cells and red cells, ghosts present in
the sample. Theoretical calculations permitted to calculate the angles Sl, s2, s3, s 4 . The detailed calculation will be reported elsewhere. These angles are: s 1 = 0,024, s 2 = 0,070, s 3 = 0,127, s 4 -- 0,300. More than eighty blood samples were tested in order to collect enough data for a statistical analysis. The samples were collected in an haematology laboratory in order to be sure not to take only healthy cases where the variations of the cell counts are not very important. For each sample we performed a platelet count with a phase-contrast microscope [4] and a white cell count with an electronic counter [5]. Each
Intensity
I
white
cells
ls
II atel6ts
E1 s1
] s2
E2
radius
E3 s3
sI
Fig. 2. Diffraction pattern of the particles.
267
Volume 10, number 3
600
ix ,
OPTICS COMMUNICATIONS
closely related to the spectrum by tile %rmula
103
/:
500
/Vp =~A" 3
N b = aK l
200
2 100 /
x I
100
200
I
300
I
'
4
40n 500 Optical c~llnt i n(,,
11) ~
I
x 10 3
g 2
10
8
6
4
2
2
'
4
a
8
"
I'0'
12
Automatic
14
co
- bE 2.
--
ntinq
Fig. 3. Leucocytes electronic counting compared with platelets phase contrast counting. sample was also diluted in an a m m o n i u m oxalate solution in order to get the red cells hemolysed. Then the sample was stirred and put into the sample holder of the diffraction device. The energies E l , t#2, E3 corresponding to the frequencies defined above were measured with a photocell located behind a hole in the Fourier-plane and the data was recorded. A regression calculation showed that the platelet number Np was 268
•
For tim calculation of Np the correlation coefficient was 0.96 and the test of Fischer (3 and 76 degrees of freedom) was about 543 denoting a high probability in favor of our initial hypothesis. The standard deviation of the difference between tile diffraction value and the optical value is 28 000 platelets pro microliter. This value is very close to the accuracy of tile platelet count itself. No discrepant values were observed and tile agreement of diffraction and count was good even for iow values. Tile white cells are calculated with even more accuracy. The correlation coefficient is 0.99 and the Fischer test (2 and 77 degrees of freedom) 1764. This may be explained by tile better reliability of leucocytes electronic counting compared with platelets phase contrast counting (fig. 3). The principle was tested on linearity. The same blood sample was diluted several times with saline water and tested like tire other samples. The diffraction values showed more linearity than manual counts especially for low counts and even more linearity than electronic counts. This may be explained by the high number of cells diffracting the beam and contributing to the signal. The diffraction method is very simple and very reliable. A device for routine use in laboratory should apply this principle in order to perform fast, accurate and reliable measurements without sample preparation.
Platelets
300
#~tq+7~'2
Tile number of white cells N b was taken in account by the formula:
400
:
March 1974
References [1] F. Michal, G.V.R. Born, Nature 231 (1971) 220- 2. [2] E.L. O'Neill, Introduction to statistical optics (AddisonWesley, Reading, Mass., 1963). [3] H.C. Van de tlulst, Light scattering by small particles (Wiley, New York, 1957). [41 G. Brecher, E.P. Cronkite, J. Appl. Physiol. 3 (1950) 365-77. [5] S. Kinsmann, J. and W. Coulter, Particle size measurement using the resistance change principle, 63th annual meeting, Toronto, april 196 I.
OPTICS COMMUNICAFIONS
March 1974
P L A T E L E T C O U N T I N G BY L I G H T D I F F R A C T I O N J.P. MERIC and J.F. CARON Ci'ntre d'Etudes et de Recherches de l 'lndustrie des Liants tt3,drauliques, 23 rue de Cronstadt, 75015 Paris, France
an d M. GOUAULT-HEILMANN and C. SULTAN Service Central d7tOnatologie-hnmunologie. Hopital Henri Mondor, 94010 Creteil. France
Received 4 January 1974 Optical properties of platelets have yet been studied by light transmission in order to follow their shape transformation. The experiments described here deal with platelet diffraction measurements performed with coherent and monochromatic laser light. The purposes of the assay which have been done, tend to demonstrate that the optical properties of platelets allow to perform counting with accuracy.
Tile device used is an optical system including a laser source, imaging lenses, a sample holder and a power spectra analyser (fig. 1). It is well known [21 that tile analysis of the light diffracted by the particles contained in tile sample holder permits to obtain statistical data about these particles. The diffracted light is measured in tile I~cal plane of the optical system, the so-called Fourierplane. It is composed of a central peak of direct light. This peak is surrounded by diffracted light which is spread around it. The Fraunhofer diffraction pattern in the Fourier-plane can be computed by Fourier transformation of the transmission and phase distribution of the array formed by the particles contained in the sample holder. The particles considered here are the blood cells of whole blood after hemolysis of the red cells. These particles are: ghosts of red cells, white cells, and platelets. The ghosts of red cells have a refraction index which is quite near to the index of the medium. This originates an amount of diffraction which is very weak for each particle but tile ghosts are very numerous and therefore the total amount of diffraction that is originated by them becomes very important. The ghosts of red cells are perfectly spherical. Their diffraction pattern can be calculated with high accuracy 266
according to the formula [3] ,S'(s)=Cf(1
e ipsinr) e ik~sd~dn,
where S is the amplitude function of the diffracted light, s is tile angle (fig. 1), k = 27r/•, X is the wavelength of the incident radiation, a is the radius of the particle, r is defined b y a 2 cos 2 7- = ~2 + n 2, and Cis a constant. Tile integral is taken over tile area of a circle with radius a. Tile intensity of tile diffraction pattern of a collection of particles is tile sum of the intensity related to each single particle if there is no overlapping in tire position of each cell. In effect there is some overlapping in position especially for ghosts of red cells. We have used a rather sophisticated mathematical model (overlapping circular grain model) to take this facl into account [21. Tile white cells are quite irregular in shape but they do not differ too much from the sphere. The size ranges from 15 to 9/ira. Light absorption in the cells is also very irregular but this may be practically neglected. Tile platelet size is 3 /lln. This dimension is near the wavelength of the light which we have used (0.63 ~m). Therefore scattering does not depend very much on the shape.
Volume 10, number 3
OPTICS COMMUNICATIONS
March 1974
diffracted light lenses
~
Et direct light
sample h o l d e r
Laser
Fig. 1. Optical system. The three kinds of particles described above scatter the light in a manner which is directly related to their size. The total diffraction pattern is the sum of the pattern of the three kinds o f particles. These patterns are described in figure 2. The horizontal axis represents the radius in the Fourier plane corresponding to the diffraction angle s. High values of the radius represent low spatial frequencies in the sample holder and low values represent very high spatial frequencies. Our experiments consisted in measuring the total energy comprised between two angles, s 1 and s 2 for example, and to relate them to the total number o f platelets, white cells and red cells, ghosts present in
the sample. Theoretical calculations permitted to calculate the angles Sl, s2, s3, s 4 . The detailed calculation will be reported elsewhere. These angles are: s 1 = 0,024, s 2 = 0,070, s 3 = 0,127, s 4 -- 0,300. More than eighty blood samples were tested in order to collect enough data for a statistical analysis. The samples were collected in an haematology laboratory in order to be sure not to take only healthy cases where the variations of the cell counts are not very important. For each sample we performed a platelet count with a phase-contrast microscope [4] and a white cell count with an electronic counter [5]. Each
Intensity
I
white
cells
ls
II atel6ts
E1 s1
] s2
E2
radius
E3 s3
sI
Fig. 2. Diffraction pattern of the particles.
267
Volume 10, number 3
600
ix ,
OPTICS COMMUNICATIONS
closely related to the spectrum by tile %rmula
103
/:
500
/Vp =~A" 3
N b = aK l
200
2 100 /
x I
100
200
I
300
I
'
4
40n 500 Optical c~llnt i n(,,
11) ~
I
x 10 3
g 2
10
8
6
4
2
2
'
4
a
8
"
I'0'
12
Automatic
14
co
- bE 2.
--
ntinq
Fig. 3. Leucocytes electronic counting compared with platelets phase contrast counting. sample was also diluted in an a m m o n i u m oxalate solution in order to get the red cells hemolysed. Then the sample was stirred and put into the sample holder of the diffraction device. The energies E l , t#2, E3 corresponding to the frequencies defined above were measured with a photocell located behind a hole in the Fourier-plane and the data was recorded. A regression calculation showed that the platelet number Np was 268
•
For tim calculation of Np the correlation coefficient was 0.96 and the test of Fischer (3 and 76 degrees of freedom) was about 543 denoting a high probability in favor of our initial hypothesis. The standard deviation of the difference between tile diffraction value and the optical value is 28 000 platelets pro microliter. This value is very close to the accuracy of tile platelet count itself. No discrepant values were observed and tile agreement of diffraction and count was good even for iow values. Tile white cells are calculated with even more accuracy. The correlation coefficient is 0.99 and the Fischer test (2 and 77 degrees of freedom) 1764. This may be explained by tile better reliability of leucocytes electronic counting compared with platelets phase contrast counting (fig. 3). The principle was tested on linearity. The same blood sample was diluted several times with saline water and tested like tire other samples. The diffraction values showed more linearity than manual counts especially for low counts and even more linearity than electronic counts. This may be explained by the high number of cells diffracting the beam and contributing to the signal. The diffraction method is very simple and very reliable. A device for routine use in laboratory should apply this principle in order to perform fast, accurate and reliable measurements without sample preparation.
Platelets
300
#~tq+7~'2
Tile number of white cells N b was taken in account by the formula:
400
:
March 1974
References [1] F. Michal, G.V.R. Born, Nature 231 (1971) 220- 2. [2] E.L. O'Neill, Introduction to statistical optics (AddisonWesley, Reading, Mass., 1963). [3] H.C. Van de tlulst, Light scattering by small particles (Wiley, New York, 1957). [41 G. Brecher, E.P. Cronkite, J. Appl. Physiol. 3 (1950) 365-77. [5] S. Kinsmann, J. and W. Coulter, Particle size measurement using the resistance change principle, 63th annual meeting, Toronto, april 196 I.